On Normal Subgroups of Product of Groups

Ashish Kumar Das

paper

On Normal Subgroups of Product of Groups

arXiv:math/0504097

Abstract

The object of this paper is to find a necessary and sufficient condition for the groups $G_{1}, G_{2}, ..., G_{n}$ so that every normal subgroup of the product $\prod_{i = 1}^{n} G_{i}$ is of the type $\prod_{i = 1}^{n} N_{i}$ with $N_{i} ⊴ G_{i}$ , $i = 1, 2, ..., n$ . As a consequence we obtain a well-known result due to R. Remak about centreless completely reducible groups having finitely many direct factors.

5 pages